The always-blunt Arrington had harsh words for both -- and others -- in an interview published in the Washington Times.
Gibbs retired for a second time from the Redskins in January.
Arrington left the Redskins in February 2006 after injuries slowed him. He signed with the New York Giants and played two months there before a ruptured Achilles tendon in October ended his career.
In 2007, he was involved in a serious motorcycle accident, but survived.
He says he has a strained relationship with Snyder.
"I think Dan Snyder is scared to death of me," Arrington said in the Times. "He won't look at me. I tried to shake his hand at [a] luncheon. He shook my hand and was like, 'How you doing, LaVar?' and kept moving. I'm probably the only person that's ever stood up to him and never backed down."
He said he tried to reach out to Snyder after the death of Sean Taylor a year ago, but was rebuffed.
"I root for the Redskins because how I feel about the fans outweighs how the organization treated me. I always take pleasure in taking jabs at Dan because people like him need that. There's got to be a person out there who's not afraid to do it."
The Times said Snyder was traveling last week and couldn't be reached for comment.
Arrington feuded with Redskins defensive coordinator Gregg Williams in 2005, his final full season. In the Times interview, he said:
"If Gregg hadn't been corrupted by the front office agenda, I probably would've had a hell of a year with him, but there were too many hidden agendas for me to be successful in that regime."
Arrington told the paper he has patched up his relationship with Williams.
Arrington is now the owner of an Annapolis, Md., sports bar. He played in 85 NFL games, picking up 411 career tackles and 23½ sacks.